Inverse problem of determining the unknown strength of an internal plane heat source

Abstract

The conjugate gradient method is used to determine the unknown timewise variation of the strength of a plane surface heat source, located at a specified position inside a flat plate, from the knowledge of transient temperature measurements taken at one of the outer surfaces while both boundary surfaces are kept insulated. The advantage of the conjugate gradient method is that no a priori information is needed on the variation of the unknown quantity. The inverse analysis is performed by using the combination of the regular and modified conjugate gradient methods. The combined method is found to be more accurate than either of these two methods for the reason discussed in this work.